Abstract

Wavefront sensing in the presence of background light sources is complicated by the need to restrict the effective depth of field of the wavefront sensor. This problem is particularly significant in direct wavefront sensing adaptive optic (AO) schemes for correcting imaging aberrations in biological microscopy. In this paper we investigate how a confocal pinhole can be used to reject out of focus light whilst still allowing effective wavefront sensing. Using a scaled set of phase screens with statistical properties derived from measurements of wavefront aberrations induced by C. elegans specimens, we investigate and quantify how the size of the pinhole and the aberration amplitude affect the transmitted wavefront. We suggest a lower bound for the pinhole size for a given aberration strength and quantify the optical sectioning provided by the system. For our measured aberration data we find that a pinhole of size approximately 3 Airy units represents a good compromise, allowing effective transmission of the wavefront and thin optical sections. Finally, we discuss some of the practical implications of confocal wavefront sensing for AO systems in microscopy.

Figures (7)

Schematic diagram of a generalized confocal wavefront sensor. Blue dashed lines show the object and intermediate image plane, red dashed lines show the pupil plane of lens L1 and its image at the wavefront sensing plane.

The effect of a circular confocal pinhole of diameter 2 AU on individual spatial frequencies in the wavefront at the WFS plane. Plots show the phase along a line (x axis) through the centre of the WFS plane for a field in the pupil plane with a sinusoidally varying wavefront (a sin(πx/l)) with an rms of (a) λ/13 and (b) λ/4 and a uniform amplitude. White lines show the geometrical cutoff frequency at 2.44 cycles / pupil.

Mean number of phase singularities in the WFS plane as a function of rms wavefront aberration for a 2 AU pinhole. Calculated from 100 pupil plane phase screens generated from a power spectral density function of the form.ckr−4 Error bars show +/− 1 standard deviation truncated at zero.

(a) Contour plot of the effective Strehl ratio due to differences in the wavefront between the WFS and pupil planes caused by the pinhole. Results shown are the mean over 100 phase screens. (b) Example showing the wavefront at the WFS plane for different pinhole sizes for a pupil plane wavefront (top) with an rms of λ/5.

(a) Mean optical section thickness versus pinhole size for pupil plane aberrations up to λ/2. (b) Example pinhole transmittance as a function of defocus for a phase screen with an rms of λ/2 (bold lines) and in the absence of aberrations in the pupil plane (faint lines).